Mateusz Wasilewski, Institute of Mathematics of the Polish Academy of Sciences
I will propose a definition of a quantum Cayley graph of a discrete quantum group. The first step will be to extend the framework of quantum graphs to a very restricted infinite dimensional setting, namely the infinite direct sums of matrix algebras. For discrete quantum groups the natural candidates for quantum adjacency matrices will be convolution operators against a projection. If this projection satisfies a symmetry condition and is generating, then it can be used to define a quantum Cayley graph. These quantum graphs to a large extent do not depend on the generating projection, just like for classical groups. In the last part of the talk I will present some examples.